Such a coffee machine is known from EP 862 883 A. The known coffee machine belongs to those coffee machines that are able to make and dispense at least two different types of coffee beverages, especially coffee beverages of the filter coffee type and coffee beverages of the espresso type. Apart from the use of preferably different types of coffee beans, these two types of coffee beverages differ from one another by a different brewing pressure, the coffee beverages of the filter coffee type being prepared under atmospheric pressure up to a slight overpressure of up to 1.5 bar, whereas coffee beverages of the espresso type need a higher pressure, i.e. one above or even clearly above 1.5 bar to about 7.5 bar. Beverages of the espresso type are only accepted by consumers if they have a very distinct, fine-pored and stable foam layer, the so-called “crema”. To this end such coffee beverage that is brewed at an increased pressure is passed in the known coffee machine through a flow path having a reduced cross-section. On the other hand, it is convenient for the consumers when both types of coffee beverages are discharged through the same tap opening, so that the user cannot put the cup or pot under the wrong outlet by mistake. In the known coffee machines, this problem is solved by interposing a device into the outlet line between brewing means and tap opening, said device reducing the outlet cross-section when coffee beverage of the espresso type is brewed, and releasing again the full cross-sectional area of the outlet when coffee beverage of the filter coffee type is brewed. This device is driven in the known coffee machine by a motor which requires additional control efforts.